If this is the case, it makes sense to ask if ⋆F∇\star F_\nabla itself is the curvature (d−(n+1))(d-(n+1))-form of a circle (d−(n+1)−1)(d-(n+1)-1)-bundle with connection ∇˜\tilde \nabla, where d=dimXd = dim X is the dimension of XX.

In the special case of ordinary electromagnetism with n=1n=1 and d=4d = 4 we have that electrically charged 0-dimensional particles couple to ∇\nabla and magnetically charged (4−(1+1)−2)=0(4-(1+1)-2) = 0-dimensional particles couple to ∇˜\tilde \nabla.

In analogy to this case one calls generally the d−n−3d-n-3-dimensional objects coupling to ∇˜\tilde \nabla the magnetic duals of the (n−1)(n-1)-dimensional objects coupling to ∇\nabla.